Underwater acoustic metamaterial based on double Dirac cone characteristics in rectangular phononic crystals**Project supported by the National Natural Science Foundation of China (Grant Nos. 11602269, 11972034, and 11802213), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB22040301), and the Research Program of Beijing, China (Grant Nos. Z161100002616034 and Z171100000817010).

Abstract

We theoretically construct a rectangular phononic crystal (PC) structure surrounded by water with C2v symmetry, and then place a steel rectangular scatterer at each quarter position inside each cell. The final complex crystal has two forms: the vertical type, in which the distance s between the center of the scatterer and its right-angle point is greater than 0.5a, and the transverse type, in which s is smaller than 0.5a (where a is the crystal constant in the x direction). Each rectangular scatterer has three variables: length L, width D, and rotation angle θ around its centroid. We find that, when L and D change and θ is kept at zero, there is always a linear quadruply degenerate state at the corner of the irreducible Brillouin zone. Then, we vary θ and find that the quadruply degenerate point splits into two doubly-degenerate states with odd and even parities. At the same time, the band structure reverses and undergoes a phase change from topologically non-trivial to topologically trivial. Then we construct an acoustic system consisting of a trivial and a non-trivial PC with equal numbers of layers, and calculate the projected band structure. A helical one-way transmission edge state is found in the frequency range of the body band gap. Then, we use the finite-element software Comsol to simulate the unidirectional transmission of this edge state and the backscattering suppression of right-angle, disorder, and cavity defects. This acoustic wave system with rectangular phononic crystal form broadens the scope of acoustic wave topology and provides a platform for easy acoustic operation.